Season the chicken breast with half of the sea salt, black pepper, and dried oregano.
Preheat a grill pan or outdoor grill to medium-high heat and lightly coat with a tiny bit of oil if needed.
Grill the chicken breast for 5-6 minutes per side until fully cooked through, then set aside to rest before slicing into strips.
Slice the halloumi cheese into 1/4-inch thick rectangles and grill for 1-2 minutes per side until golden brown char marks appear.
In a large bowl, combine the chopped romaine, cucumber, halved cherry tomatoes, thinly sliced red onion, and olives.
In a small jar or bowl, whisk together the extra virgin olive oil, lemon juice, and the remaining oregano, salt, and pepper.
Drizzle the dressing over the vegetables and toss gently to coat.
Top the salad with the sliced grilled chicken and warm halloumi cheese slices to serve.